Charles and the Queen Consort, whose coronation will take place on May 6, a few days before the competition, also met Britain's entrant Mae Muller and took part in the recording of a segment for the children's television entertainment show Blue Peter.
"We'll be watching with great interest, egging you on," the King told Muller on Wednesday.
Liverpool is set to host the competition, on behalf of last year's winner Ukraine after it was unable to stage the competition because of the Russian invasion.
Britain was the runner-up last year.
Following a countdown by onlookers, Charles and Camilla unveiled the competition stage by pressing a large pink button which initiated a series of colourful dancing stage lights and a pulsating beat.
Next month will see a series of celebrations across Britain, with the formal coronation ceremony for Charles at Westminster Abbey and a concert the following day after at Windsor Castle.
In February, Britain's government said it would make 3000 tickets for the Eurovision Song Contest available to displaced Ukrainians and provide £10 million ($NZ20.3 million) of funding to help host the competition.
